- #1
whozum
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For a function f(x,y): The error is:
\Delta f(x,y) = \sqrt{(\frac{df}{dx})^2+(\frac{df}{dy})^2}
Is this a form of the approximation in algebraic error determination:
\Delta f(x,y) = \sqrt{f(x+\Delta x,y) + f(x,y+\Delta y)}?
Now I was trying to do this in my bio lab for genetics and probability distribution. We had 27 samples, predicted 75% (20.25) to be purple and 25% (6.75) to be white. We observed that 23 were purple and 4 were white, so to calculate the deviation I used the above function and got:
\frac{df}{dx} = \frac{23-20.25}{20.25}, \frac{df}{dy} = \frac{4-6.75}{6.75}
*For some reason latex doesn't want to show it, but I plugged in my numbers into the first equation above.
So the observed sample was 18.44% off?
They gave us an equation to find the deviation of a population from the expected value which is similar to the one above:
\chi^2 = {\frac{(Obs_p - Exp_p)}{Exp_p}^2+\frac{(Obs_w - Exp_w)}{Exp_w}^2}
\chi^2 = {\frac{(2.75)}{20.25}^2+\frac{(2.75)}{6.75}^2} = 1.494
It claims that "If the value for chi squared is less than or equal to 3.841, then your sample is within the expected range."
Is this a standard deviation?
This is pretty similar to the first equation, except we're squaring the numerator instead of the whole fraction. Did I get my error equation wrong, or are these truly diferent and unlinked?
\Delta f(x,y) = \sqrt{(\frac{df}{dx})^2+(\frac{df}{dy})^2}
Is this a form of the approximation in algebraic error determination:
\Delta f(x,y) = \sqrt{f(x+\Delta x,y) + f(x,y+\Delta y)}?
Now I was trying to do this in my bio lab for genetics and probability distribution. We had 27 samples, predicted 75% (20.25) to be purple and 25% (6.75) to be white. We observed that 23 were purple and 4 were white, so to calculate the deviation I used the above function and got:
\frac{df}{dx} = \frac{23-20.25}{20.25}, \frac{df}{dy} = \frac{4-6.75}{6.75}
*For some reason latex doesn't want to show it, but I plugged in my numbers into the first equation above.
So the observed sample was 18.44% off?
They gave us an equation to find the deviation of a population from the expected value which is similar to the one above:
\chi^2 = {\frac{(Obs_p - Exp_p)}{Exp_p}^2+\frac{(Obs_w - Exp_w)}{Exp_w}^2}
\chi^2 = {\frac{(2.75)}{20.25}^2+\frac{(2.75)}{6.75}^2} = 1.494
It claims that "If the value for chi squared is less than or equal to 3.841, then your sample is within the expected range."
Is this a standard deviation?
This is pretty similar to the first equation, except we're squaring the numerator instead of the whole fraction. Did I get my error equation wrong, or are these truly diferent and unlinked?
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